From the particle physics point of view, the Higgs portal interaction is usually invoked to solve stability issues of the Standard Model. In this context, let us note that corrections from the portal term can indeed stabilise the potential [1]}, [2]}, [3]}. These issues are particularly relevant when considering the inflationary period [4]}. It has been also established that for the model we discuss here with \(\eta \)  and \(\phi \)  developing non-vanishing vevs, the \(\phi -\eta \)  portal term induces oscillations between the two scalars in our model [5]}, [6]}.
